I always interpret "upkeep" as another way of expressing "maintenance".
example... My house is old, so there is a bit of upkeep to do for it.
Substitute "bike" for "house" and you get the same meaning...
My bike is old, so there is a bit of upkeep to do for it.
As far as your second sentence, sounds like you are trying to use "going on"?
There is a lot "going on" with this problem.
In this case, it expresses a lot of "activity" occurring.
Secondary thought... it can be used to express a casual greeting, too.
"Hey, what's going on"?
(Which is a more informal way to say "What's happening?")